You know you’re in the hands of a great filmmaker when sparks fly off the screen as a waitress takes someone’s elaborate breakfast order. The scene in question occurs early in Paul Thomas Anderson’s Phantom Thread, which is set in London during the late 1950s and quickly establishes its male lead, fashion designer Reynolds Woodcock (Daniel Day-Lewis), as a control freak and serial womanizer, prone to casually discard paramours the moment they cease to excite him. Actually, Reynolds leaves the dirty work to his sister Cyril (Lesley Manville), who serves as a combination assistant/enabler, as well as his only apparent friend.

One day, newly unattached, Reynolds drives out to the country, where he maintains a house, and dines at a restaurant, where a waitress named Alma (Vicky Krieps) catches his eye … and he, hers. Their initial flirtation consists almost entirely of Reynolds ordering, with intimidating specificity, what seems like half of the breakfast menu, as Alma, only slightly flustered, meets his gaze and matches his wit.

This unconventional meet-cute kicks off one of the most perverse romances in recent memory. In fact, it’s so offbeat that its shape remains (pleasantly) amorphous for quite some time. Anderson loves doing research for his period pieces, and he delves into many details of British fashion during that era (though he was initially inspired by Spanish designer Cristóbal Balenciaga), making the film seem vaguely like a biopic. Cyril’s unmistakable physical resemblance to Rebecca’s Mrs. Danvers, coupled with both characters occupying roughly the same disdainfully watchful spot in their respective narratives, suggests that the film might evolve into a thriller. Only toward the end does Anderson’s long game finally become apparent. To reveal much more would be criminal—suffice it to say that Phantom Thread depicts a singular battle of wills between two evenly matched and equally ruthless combatants, and resolves in a truly unexpected way.

Anderson previously directed Day-Lewis to his second Oscar (of three) in There Will Be Blood, and the actor has announced that this will be his final performance. That’s a great loss to cinema, but it’s entirely apt that he bows out opposite a relative newcomer who’s afforded a star-making turn here. The superficial gulf in power between Alma and Reynolds deliberately echoes that between Krieps (who hails from Luxembourg and has previously played only small roles in English-language films) and Day-Lewis; both Alma and Krieps have to hold their own in daunting circumstances, and both succeed magnificently.

Anderson, for his part, works in a statelier (but no less visually ravishing) mode than usual, shooting on 35mm film and replicating the slightly soft look of vintage Merchant Ivory costume dramas. If this does turn out to be Day-Lewis’ swan song, at least he goes out on a high note.